Hamilton-Jacobi equations : approximations, numerical analysis and applications : Cetraro, Italy 2011 / Yves Achdou [and others] ; editors: Paola Loreti, Nicoletta Anna Tchou.

By: Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications (Summer School) (2011 : Cetraro, Italy)
Contributor(s): Achdou, Yves | Loreti, Paola | Tchou, Nicoletta Anna
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 2074.Publisher: Berlin ; New York : Springer, ©2013Description: 1 online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783642364334; 3642364330; 3642364322; 9783642364327Subject(s): Hamilton-Jacobi equations -- Congresses | Hamilton-Jacobi equations | Mathematics | Functional equations | Differentiable dynamical systems | Differential equations, partial | Mathematical optimization | Calculus of Variations and Optimal Control; Optimization | Partial Differential Equations | Computational Mathematics and Numerical Analysis | Game Theory, Economics, Social and Behav. Sciences | Dynamical Systems and Ergodic Theory | Difference and Functional EquationsGenre/Form: Electronic books. | Conference papers and proceedings. Additional physical formats: Printed edition:: No titleDDC classification: 515/.64 LOC classification: QA316 | .C56 2011Online resources: Click here to access online
Contents:
Finite Difference Methods for Mean Field Games / Yves Achdou -- An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton-Jacobi Equations and Applications -- A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations / Hitoshi Ishii -- Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations / Grigory L. Litvinov.
Summary: These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).
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Finite Difference Methods for Mean Field Games / Yves Achdou -- An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton-Jacobi Equations and Applications -- A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations / Hitoshi Ishii -- Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations / Grigory L. Litvinov.

Includes bibliographical references.

These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).

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